Lifting off from Andrews Air Force Base outside Washington, Obama headed for Havana where the sight of Air Force One, America's iconic presidential jet, touching down on Cuban soil would have been unimaginable not long ago.

The three-day trip, the first by a US president in 88 years, is the culmination of a diplomatic opening announced by Obama and Cuban President Raul Castro in December 2014, ending a Cold War-era estrangement that began when the Cuban revolution ousted a pro-American government in 1959.

Obama, who abandoned a longtime US policy of trying to isolate Cuba internationally, now wants to make his shift irreversible. But major obstacles remain to full normalization of ties.

Ahead of Obama's arrival, plainclothes police blanketed the capital with security while public works crews busily laid down asphalt in a city where drivers joke they must navigate "potholes with streets."

Welcome signs with images of Obama alongside Castro popped up in colonial Old Havana, where the president and his family will tour later on Sunday.

Since rapprochement, the two sides have restored diplomatic ties, signed commercial deals on telecommunications and scheduled airline service.

"Obama has been brave for agreeing to relations with Cuba," said school teacher Elena Gonzalez, 43.

Major differences remain, notably the 54-year-old economic embargo of Cuba. Obama has asked Congress to rescind it but has been blocked by the Republican leadership.

Instead, he has used executive authority to loosen trade and travel restrictions to advance in normalizing relations with Cuba, one of his top foreign policy priorities along with the Iran nuclear deal.

Cuba also complains about the continued occupation of the naval base at Guantanamo Bay, which Obama has said is not up for discussion, as well as US support for dissidents and anti-communist radio and TV programs beamed into Cuba.

Speaking to reporters, foreign trade and foreign investment minister Rodrigo Malmierca DÃ­az said Obama's regulatory moves "go in the right direction." But he added: "We can't reach a normalization of relations with the blockade still in effect and without resolving other themes of high importance."

Echoing the official line, Ileana Valdes, 55, a nurse, said: "There are many years of mistrust and we are not going to change our system, our values. Although one must highlight that there are no longer invasions."